Yes, you should have the internet at home if you are the CTO and the only team member with expertise in scaling or systems.

But you shouldn't be the 5% equity CTO who is responsible for the scaling with two non-technical co-founders in the first place. Especially if you are a guy who likes to be away from the internet.

Make the company pay for it.

Personally, I agree with your viewpoint and am not having internet at home when I move into my next apartment. But I am also not the CTO of a startup.

Also, I feel the need to say "A startup with two business guys and a CTO who hates the internet: 'Only in New York...'"